Universal Polar Coding for Parallel Gaussian Channels with Non-Binary Inputs and Its Applications to HARQ and MIMO

In this paper, we first propose an universal polar coding scheme for parallel Gaussian channels with non-binary inputs. It is assumed that the encoder knows only the sum capacity of M parallel channels instead of the capacity of any single channel. By decomposing each parallel channel into T = [log2r] sub channels, we therefore obtain MT binary sub-channels. A super polar coding scheme that across all sub-channels is then proposed. This scheme can achieve the sum capacity when the block length is sufficiently large. We have also discussed the applications of parallel polar coding design for both the HARQ and MIMO systems. It is shown that a capacity-achieving HARQ scheme can be obtained for block fading channel and a capacity-achieving MIMO design that requires only the feedback of the sum rate of all MIMO layers can also be attained.